The Annals of Statistics

A complementary set theory for quaternary code designs

Rahul Mukerjee and Boxin Tang

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Abstract

Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number of factors. This is in contrast to existing theoretical results which work only for a relatively small number of factors. While the use of imaginary numbers to represent the Gray map associated with QC designs facilitates the derivation, establishing a link with foldovers of regular fractions helps in presenting our results in a neat form.

Article information

Source
Ann. Statist., Volume 41, Number 6 (2013), 2768-2785.

Dates
First available in Project Euclid: 17 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1387313389

Digital Object Identifier
doi:10.1214/13-AOS1160

Mathematical Reviews number (MathSciNet)
MR3161447

Zentralblatt MATH identifier
1292.62119

Subjects
Primary: 62K15: Factorial designs

Keywords
Foldover Gray map highly fractionated design minimum aberration minimum moment aberration projectivity resolution

Citation

Mukerjee, Rahul; Tang, Boxin. A complementary set theory for quaternary code designs. Ann. Statist. 41 (2013), no. 6, 2768--2785. doi:10.1214/13-AOS1160. https://projecteuclid.org/euclid.aos/1387313389


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